Among lithium secondary batteries employing various cathode active materials, those employing V.sub.6 O.sub.13, a vanadium oxide, as the active material, are characterized as having large discharge capacities but have a drawback of being low in discharge voltage. Those employing V.sub.2 O.sub.5 as the active material show high discharge voltages but are disadvantageous in that the discharge curves are two-level curves. Those employing V.sub.6 O.sub.13 and V.sub.2 O.sub.5 are disadvantageous in that the charge discharge cycle in 100% depth is weak. Those employing metal oxide composite compounds such as amorphous V.sub.2 O.sub.5 or amorphous V.sub.2 O.sub.5 and Co.sub.2 O.sub.3 (JP-A-1-231271) are good in charge-discharge cycle characteristics but they are disadvantageous in that discharge capacities are low and the evenness of the discharge curves are not sufficient. Those employing composite compounds in which 5 to 10 mol % of oxides such as Co.sub.3 O.sub.4 is added to V.sub.2 O.sub.5 (JP-A-2-12768) have high discharge capacities but the charge-discharge cycle characteristics are practically insufficient. Those employing spinel-type LiMn.sub.2 O.sub.4 as the active material show poor charge-discharge cycle characteristics, and consequently, an improvement in this respect is desired. In addition, though it is well known to use LiCoO.sub.2 as an cathode active material in a lithium battery (JP-A-52-12424, JP-A-60-127669, U.S. Pat. Nos. 3,945,848, 4,340,652, and 4,567,061), LiCoO.sub.2 is high charge potential and oxidative degradates an electrolytic solution, then the charge-discharge cycle characteristics is insufficient, and consequently, an improvement in this respect is desired. JP-A-62-256371 discloses composite oxides represented by LiMO.sub.2 (M.dbd.Co, Ni, V, Cr, Fe) and discloses that among them LiMO.sub.2 is a layer rock salt crystalline structure such as LiCoO.sub.2, and further, it relates to a primary battery. (The term "JP-A" as used herein means an "unexamined published Japanese patent application".)